Quantum thermodynamics of nanoscale steady states far from equilibrium

TL;DR

This paper develops an exact quantum thermodynamic framework for nanoscale steady states far from equilibrium, linking quantum transport phenomena with thermodynamic principles and extending classical relations to the quantum regime.

Contribution

It introduces a steady-state thermodynamic function that captures quantum transport in multiterminal systems and derives nonlinear Onsager relations for such nonequilibrium states.

Findings

Explicit form of thermodynamic function for single bosonic or fermionic level

Identification of thermodynamic forces (affinities) in quantum transport

Extension of Onsager reciprocity to nonlinear quantum regimes

Abstract

We develop an exact quantum thermodynamic description for a noninteracting nanoscale steady state that couples strongly with multiple reservoirs. It is demonstrated that there exists a steady-state extension of the thermodynamic function that correctly accounts for the multiterminal Landauer-B\"{u}ttiker formula of quantum transport of charge, energy or heat, via the nonequilibrium thermodynamic relations. Its explicit form is obtained for a single bosonic or fermionic level in the wide-band limit, and corresponding thermodynamic forces (affinities) are identified. Nonlinear generalization of the Onsager reciprocity relations are derived. We suggest that the steady-state thermodynamic function is also capable of characterizing the heat current fluctuations of the critical transport where the thermal fluctuations dominate. It is also pointed out that the suggested nonequilibrium steady-state thermodynamic relations seemingly persist for a spin-degenerate single level with local interaction.